Quantum mechanical systems have been investigated for numerous applications known as quantum information processing including quantum computation, quantum communication and quantum cryptography. A quantum system can be used to store and very efficiently process information which is carried in its two-state quantum subsystems, called quantum bits or “qubits.” The computation and information processing based on quantum mechanical principles can outperform classical computation and information processing in a number of tasks like database search and prime factorization problems.
A quantum computer is particularly attractive tool if it is “universal,” that is, capable of solving any computable task. Quantum computation is known to be universal as long as arbitrary single-qubit and non-local (entangling) two-qubit unitary operations can be applied in an arbitrarily structured sequence called a quantum circuit. These operations are a result of the physical structure of the system and control fields applied on it, which both are embodied in the Hamiltonian of the system. Universality is thus determined fundamentally by the physical structure of the qubit implementation and by control of this with clear distinction between controlling an interaction that is intrinsic to the system, and introducing a new interaction with an external control field. In many of the possible physical implementations (for details on proposed implementations, see for instance S. L. Braunstein and H. K. Lo, “Scalable quantum computers, paving the way to realization”, Wiley-VCH, 2001), the inherent physical interactions do not suffice to generate the universal set of quantum computing operations over physical qubits and must be supplemented by such additional. external Hamiltonian control terms. This may introduce demanding nanoscale engineering constraints as well as additional unwanted sources of decoherence (i.e. a noise process which destroys the effectiveness of a quantum computer). Consequently, the question of whether and how we can use a particular physical system containing some very specific, non-generic interactions, for universal quantum computation has become very relevant with increasing technological effort in the area of implementation of quantum computation.
The solution of the problem of a lack of universality of numerous intrinsic physical interactions can be constructed by a suitable encoding of the states representing quantum logic into a two and higher dimensional subspace of the system Hilbert space. This concept is called “encoded universality”. The significance of the encoded universality schemes for quantum computation lies in the fact that they require active manipulation of only two-particle exchange interactions, and hence can be generically referred to “exchange-only computation”, and hence avoid other sources of decoherence like application of additional control fields. They are closely related to numerous proposals for quantum computation in solid state systems in which the exchange interaction is a common feature.